To narrow down what model you have, what does the bottom look like? Does it have a removable battery, or is it sealed in under a slightly rubbery bottom piece?

My thought is that if it's the sealed in model, OS X 10.6.0 is too old to support the hardware, but close enough the installer ran. I think those models shipped with 10.6.1 or 10.6.2 if it was from late 2009.

Do you have the ability to plug in the SSD to the other machine you have easily? Could always do the 10.6 install there, update it, then move it back to the Macbook.